Information on Result #737012
Linear OA(3216, 6616, F3, 38) (dual of [6616, 6400, 39]-code), using construction X applied to Ce(37) ⊂ Ce(30) based on
- linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(315, 55, F3, 6) (dual of [55, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3218, 6618, F3, 38) (dual of [6618, 6400, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3219, 6619, F3, 38) (dual of [6619, 6400, 39]-code) | [i] | ||
| 3 | Linear OA(3220, 6620, F3, 38) (dual of [6620, 6400, 39]-code) | [i] | ||
| 4 | Linear OA(3221, 6621, F3, 38) (dual of [6621, 6400, 39]-code) | [i] | ||
| 5 | Linear OOA(3216, 5014, F3, 2, 38) (dual of [(5014, 2), 9812, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3216, 5014, F3, 3, 38) (dual of [(5014, 3), 14826, 39]-NRT-code) | [i] | ||
| 7 | Linear OOA(3216, 5014, F3, 4, 38) (dual of [(5014, 4), 19840, 39]-NRT-code) | [i] | ||
| 8 | Linear OOA(3216, 5014, F3, 5, 38) (dual of [(5014, 5), 24854, 39]-NRT-code) | [i] | ||
| 9 | Digital (178, 216, 5014)-net over F3 | [i] | ||
| 10 | Linear OA(3220, 6622, F3, 38) (dual of [6622, 6402, 39]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OOA(3216, 3308, F3, 2, 38) (dual of [(3308, 2), 6400, 39]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3216, 2205, F3, 3, 38) (dual of [(2205, 3), 6399, 39]-NRT-code) | [i] | ||
| 13 | Linear OOA(3216, 1654, F3, 4, 38) (dual of [(1654, 4), 6400, 39]-NRT-code) | [i] | ||
| 14 | Linear OOA(3216, 1323, F3, 5, 38) (dual of [(1323, 5), 6399, 39]-NRT-code) | [i] | ||